ABSTRACT
For modeling censored time-to-event or survival data, the Cox proportional hazards model (PHM) [1,2] is most popular among the practitioners. However, the Cox PHM may not be appropriate for certain survival data such as those from the population, in which a significant proportion of patients are cured. Due to the recent medical advance, a significant proportion of patients are cured from various types of cancers such as breast cancer, head and neck cancer, melanoma, and prostate cancer. Thus, survival data in particular from cancer clinical trials often have a cure fraction. A cure rate model is particularly suitable for modeling these types of survival data as in the cure rate model, we assume that a certain fraction of the population is cured and the corresponding hazard is zero. There has been a vast literature on the cure rate models, including Berkson and Gage [3], Farewell [4,5], Halpern and Brown [6,7], Meeker [8], Kuk and Chen [9], Laska and Meisner [10], Yamaguchi [11], Yakovlev et al. [12], Yakovlev [13], Meeker and LuValle [14], Taylor [15], Asselain et al. [16], Fine [17], Chen et al. [18], Sy and Taylor [19], Peng and Dear [20], Broet et al. [21], Chen and Ibrahim [22,23], Ibrahim et al. [24], Tsodikov [25,26], Chen et al. [27, 28, 29], Ibrahim et al. [30], Yin and Ibrahim [31,32], Chi and Ibrahim [33], Kim
et al. [34], and Cooner et al. [35]. Berkson and Gage [3] first introduced the mixture cure rate model. An extensive discussion of frequentist methods of inference for the mixture cure rate model is given in Maller and Zhou [36]. Bayesian formulation of the cure rate model is discussed in Ibrahim et al. ([37], Chapter 5). Tsodikov et al. [38] gave an excellent review on estimating cure rates from both frequentist and Bayesian perspectives. In this chapter, we primarily focus on the cure-rate models with applications to
melanoma and prostate cancer data. Melanoma is the most serious type of cancer of the skin. About 62,000 new cases are diagnosed in the United States each year, and there are about 8000 melanoma deaths. When caught early, melanomas can be easily treated by surgically removing the cancerous patch of skin. Prostate cancer forms in tissues of the prostate (a gland in the male reproductive system found below the bladder and in front of the rectum). Prostate cancer usually occurs in older men. About 186,320 new cases are diagnosed in the United States each year and there are about 28,000 deaths from prostate cancer. When cancer is detected before it spreads beyond the region of the prostate, it can be cured (completely eradicated for the remaining life of the patient) in many patients using treatment techniques that are widely available in the United States today. Although prostate cancer is the second leading cause of cancer death in men. Only 1 man in 34 will die of prostate cancer. As melanoma and prostate cancer can be cured, the cure rate model may be more suitable than the Cox PHM for modeling survival data from melanoma or prostate cancer clinical trials. In this chapter, we consider two such data sets, one from the E1673 trial conducted by Eastern Cooperative Oncology Group (ECOG) and another from a retrospective cohort study of 353 men treated with conventional-dose external beam radiation therapy (RT) at St. Anne’s Hospital in Fall River, MA to examine whether the cure rate models fit these data better than the Cox PHM. The rest of this chapter is organized as follows. A detailed description of the data
is given in Section 15.2. Section 15.3 presents the development of cure rate models. The analysis of the data is carried out in detail in Section 15.4. We conclude this chapter with a brief discussion in Section 15.5.
